Method: Recently sample size formulae were presented1for estimating treatment, selection (the difference in outcomes for participants who prefer one treatment compared to the other) and preference effects (the difference in outcomes for participants who receive their preferred treatment compared to those who do not receive their preferred treatment). We have reviewed the literature to understand the design issues that can occur when participant choice is incorporated into randomised trials and used a hypothetical example to demonstrate how these impact the sample size and power calculations.
Result: In our hypothetical example we would require a sample of size 300 participants to have 80% power (5% significance level) to detect a moderate to large preference or selection effect when the treatments are equally preferred. We have also shown that the preference rate for one treatment compared to the other has a large impact on the power of the study. If 70% of the participants preferred one treatment compared to the other then the sample size increases to a total of 470 to maintain 80% power, a substantial increase. It is also possible that some participants will be unable to decide between the two treatments, this reduces the power by decreasing the number of participants who have a preference and whose information feeds into the estimation of the selection and preference effects.
Conclusion: We have shown that the preference rate for one treatment compared to the other and ensuring a very high proportion of participants (in the choice arm) are able to make a choice are key aspects of ensuring that the study is adequately powered. Careful piloting will ensure any issues with these assumptions are identified and adjusted for and information on the preference rate is available prior to undertaking these trials.
References:
1) Turner et al. Sample size and power when designing a randomised trial for the estimation of treatment, selection and preference effects. In Press Medical Decision Making.